Schur functions for approximation problems

TL;DR

This paper introduces a novel combinatorial approach using Schur functions for least squares approximation, demonstrating practical applications like curve clustering and offering an alternative to traditional algebraic methods.

Contribution

The paper presents a new combinatorial method based on Schur functions for approximation problems, contrasting with existing algebraic approaches.

Findings

Effective in curve clustering applications

Provides a new perspective on approximation problems

Highlights combinatorial advantages over algebraic methods

Abstract

In this paper we propose a new approach to least squares approximation problems. This approach is based on partitioning and Schur function. The nature of this approach is combinatorial, while most existing approaches are based on algebra and algebraic geometry. This problem has several practical applications. One of them is curve clustering. We use this application to illustrate the results.